In patent application WO2005SE01619 (publication number WO2007050001) a method is described wherein line constants of a telecommunications transmission line are estimated using estimates of the line input impedance Zin at a number of angular frequencies ω as input values. Values of Zin for at least two angular frequencies ω are required in order to estimate the line constants {circumflex over (R)} (line resistance), {circumflex over (L)} (line inductance) and Ĉ (line capacitance). (line conductance Ĝ neglected)
Zin is expressed as a polynomial in jω with the line constants as coefficients. This relationship is solved for the line constants by means of two systems of equations, where in each system there is one equation per spectral component of Zin, i.e. at least two equations per system.
Only spectral components of Zin for which the propagation constant of the line times the line length is less than π (|γd|<π or |Γ|<π) can be used.
The estimates so obtained suffer from some inaccuracy, in particular the inductance estimate has an accuracy of about 30%.
The disclosure suggests that better accuracy can be achieved by using more frequencies, i.e. measuring Zin at more frequencies and using these values as input.
In GB 2180073 A (corresponding to FR 2586818 A), a method for detecting wear in underwater cables is disclosed. The primary parameters of the cable are measured before deployment of the cable and, using the propagation constant (calculated from the measured primary parameters) as an intermediate value, an input impedance Za of the line in good condition is determined.
When the apparent impedance Za changes, a model is applied in which a position and impedance of a fault are varied until the Za calculated according to the model matches the measured Za, and hence the fault position and impedance used as input for the model correspond to the position and impedance of the actual fault or wear point.
U.S. Pat. No. 4,313,169 discloses a system for detecting the position of a fault in an electrical power line. Current and voltage measurements, along with the propagation constant and characteristic impedance of the line are used to estimate the location of a fault. The propagation constant and characteristic impedance are assumed to be known a priori. It is assumed that both the resistance and the conductance per unit length are negligible.